How to show that if $X=M oplus N$ is a Banach space then $exists c > 0$ $forall min M , forall nin N:...
Let $X=M oplus N$, where $X$ is a Banach space and $M$ and $N$ are closed subspaces of $X$.
How to prove that $exists c > 0$ constant such that $forall m in M$ and $forall n in N$ $$ leftlVert mrightrVert + leftlVert nrightrVert leq c leftlVert m + nrightrVert$$?
functional-analysis banach-spaces direct-sum
asked Nov 25 at 19:58
kaxuzibum
163
closed as off-topic by amWhy, Saad, jgon, Chinnapparaj R, user10354138 Nov 26 at 8:13
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Let $X=M oplus N$, where $X$ is a Banach space and $M$ and $N$ are closed subspaces of $X$.
How to prove that $exists c > 0$ constant such that $forall m in M$ and $forall n in N$ $$ leftlVert mrightrVert + leftlVert nrightrVert leq c leftlVert m + nrightrVert$$?
functional-analysis banach-spaces direct-sum
asked Nov 25 at 19:58
kaxuzibum
163
closed as off-topic by amWhy, Saad, jgon, Chinnapparaj R, user10354138 Nov 26 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Saad, jgon, Chinnapparaj R, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Let $X=M oplus N$, where $X$ is a Banach space and $M$ and $N$ are closed subspaces of $X$.
How to prove that $exists c > 0$ constant such that $forall m in M$ and $forall n in N$ $$ leftlVert mrightrVert + leftlVert nrightrVert leq c leftlVert m + nrightrVert$$?
functional-analysis banach-spaces direct-sum
asked Nov 25 at 19:58
kaxuzibum
163
Let $X=M oplus N$, where $X$ is a Banach space and $M$ and $N$ are closed subspaces of $X$.
How to prove that $exists c > 0$ constant such that $forall m in M$ and $forall n in N$ $$ leftlVert mrightrVert + leftlVert nrightrVert leq c leftlVert m + nrightrVert$$?
functional-analysis banach-spaces direct-sum
functional-analysis banach-spaces direct-sum
asked Nov 25 at 19:58
kaxuzibum
163
asked Nov 25 at 19:58
kaxuzibum
163
asked Nov 25 at 19:58
kaxuzibum
163
asked Nov 25 at 19:58
kaxuzibum
163
asked Nov 25 at 19:58
kaxuzibum
163
163
closed as off-topic by amWhy, Saad, jgon, Chinnapparaj R, user10354138 Nov 26 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Saad, jgon, Chinnapparaj R, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by amWhy, Saad, jgon, Chinnapparaj R, user10354138 Nov 26 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Saad, jgon, Chinnapparaj R, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
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Try showing boundedness of the projection operators $P(m+n) = m$ and $Q(m+n) = n$ by the use of, for instance, closed graph theorem. This will show that $|m| leq c_1|m + n|$ and $|n| leq c_2|m+n|$.
answered Nov 25 at 20:27
Bartosz Malman
8011620
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1 Answer
1
active
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votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Try showing boundedness of the projection operators $P(m+n) = m$ and $Q(m+n) = n$ by the use of, for instance, closed graph theorem. This will show that $|m| leq c_1|m + n|$ and $|n| leq c_2|m+n|$.
answered Nov 25 at 20:27
Bartosz Malman
8011620
add a comment |
Try showing boundedness of the projection operators $P(m+n) = m$ and $Q(m+n) = n$ by the use of, for instance, closed graph theorem. This will show that $|m| leq c_1|m + n|$ and $|n| leq c_2|m+n|$.
answered Nov 25 at 20:27
Bartosz Malman
8011620
add a comment |
Try showing boundedness of the projection operators $P(m+n) = m$ and $Q(m+n) = n$ by the use of, for instance, closed graph theorem. This will show that $|m| leq c_1|m + n|$ and $|n| leq c_2|m+n|$.
answered Nov 25 at 20:27
Bartosz Malman
8011620
Try showing boundedness of the projection operators $P(m+n) = m$ and $Q(m+n) = n$ by the use of, for instance, closed graph theorem. This will show that $|m| leq c_1|m + n|$ and $|n| leq c_2|m+n|$.
answered Nov 25 at 20:27
Bartosz Malman
8011620
answered Nov 25 at 20:27
Bartosz Malman
8011620
answered Nov 25 at 20:27
Bartosz Malman
8011620
answered Nov 25 at 20:27
Bartosz Malman
8011620
8011620
add a comment |
add a comment |
